Use our free GCF of Fractions Calculator tool to compute the GCF of 1/87, 60/71, 97/174, 123/742 i.e 1/4583334 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1/87, 60/71, 97/174, 123/742.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1/87,60/71,97/174,123/742
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 1/87,60/71,97/174,123/742, numerators are 1,60,97,123
Denominators are 87,71,174,742
The GCF of 1,60,97,123 is 1 .
LCM of 87,71,174,742 is 4583334.
The greatest common factor of 1/87,60/71,97/174,123/742 = [GCF of 1,60,97,123]/[LCM of 87,71,174,742]= 1/4583334
Therefore, the GCF of 1/87,60/71,97/174,123/742 is 1/4583334.
To find the highest common factor of 1,60,97,123, we have to find the factors of both numbers and list the highest common factor.
The factors of 1 are 1
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 97 are 1, 97
The factors of 123 are 1, 3, 41, 123
The HCF of 1,60,97,123 is 1.
Lets's calculate GCF of 1,60,97,123
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 1
:1
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 97
:1,97
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 1,60,97,123 . The biggest common factor number is the GCF number.
So the greatest common factor 1,60,97,123 is 1.
Lets's calculate LCM of 87,71,174,742
2 | 87, 71, 174, 742 |
3 | 87, 71, 87, 371 |
29 | 29, 71, 29, 371 |
1, 71, 1, 371 |
∴ So the LCM of the given numbers is 2 x 3 x 29 x 1 x 71 x 1 x 371 = 4583334
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4583334
Therefore, the GCF of Fractions 1/87,60/71,97/174,123/742 is 1/4583334
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 87,71,174,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(87,71,174,742) = 1
common factors(in case of two or more numbers have common factors) = 174
GCF(87,71,174,742) x common factors =1 x 174 = 174
LCM(87,71,174,742) = ( 87 × 71 × 174 × 742 ) / 174
LCM(87,71,174,742) = 797500116 / 174
LCM(87,71,174,742) = 4583334
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 1,60,97,123?
The HCF of 1,60,97,123 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 1/87, 60/71, 97/174, 123/742?
Answer: GCF of Numerators as per given numbers 1/87, 60/71, 97/174, 123/742 is
GCF of Numerators i.e. for 1,60,97,123 is 1
LCM of denominators i.e. for 87,71,174,742 is 4583334.
Thus, GCF of Fractions is 1/4583334.Finally, GCF of Fractions for 1/87, 60/71, 97/174, 123/742 is 1/4583334.